Wireless communications based on multiple antennas is a very promising technique which is subject to extensive investigations so as to take into advantage of the significant increase of data rate which may be obtained by such technique.
FIG. 1 illustrates a basic 2×2 multiple-Input Multiple Output (MIMO) spatial multiplexing communication between an emitter 10 and a receiver 20, and the processing of a single data flow—represented by reference 1—which is divided into two distinctive data streams 2 and 3 by means of a multiplexer 15 and each subflows are then being processed by a respective modulator and RF circuit (resp. 13 and 14) before being conveyed to two transmit antennas 11 and 12.
On the receiver side, two antennas 21 and 22 provides two RF signals which are received by receiver 20 which performs RF reception, demodulation and then detection of the two data streams before multiplexing it into one single data stream.
The MIMO configuration allows to get rid of the different obstacles (such as represented by obstacles 28 and 29 in figures) and thus increase the data rate of the communication.
Now considering the receiver of the communication, let us introduce a nT-transmit and nR-receive nT×nR MIMO system model such as: y=Hx+n, where y is the receive symbols vector, H the channel matrix, x the transmit symbols vector and n an additive white Gaussian noise.
Reduction of complexity in the MIMO detection can be achieved both by means of Sphere Decoders techniques or lattice reductions.
A first well known technique for finding the optimal Maximum Likelihood (ML) estimate {circumflex over (x)}ML by avoiding an exhaustive search is to examine only the lattice points that lie inside a sphere. This solution is denoted as the Sphere Decoder (SD) technique and, starting from the conventional ML equation
                                                                        x                ^                            ML                        =                                          argmin                                  x                  ∈                                      ξ                                          n                                              T                        ⁢                                                                                                                                                                                  ⁢                                                                                      y                    -                    Hx                                                                    2                                              ,                      it            ⁢                                                  ⁢            reads            ⁢                          :                                      ⁢                                  ⁢                                                            x                ^                            SD                        =                                          argmin                ⁢                                                                                                                                                  Q                          H                                                ⁢                        y                                            -                      Rx                                                                            2                                            ≤                              d                2                                              ,                                    (        1        )            
where H=QR, with the classical QR Decomposition (QRD) definitions, and d is the sphere constraint.
The SD principle has been introduced and leads to numerous implementation problems. In particular, it is a NP-hard problem. This aspect has been partially solved through the introduction of an efficient solution that lies in a Fixed Neighbourhood Size Algorithm (FNSA), commonly denoted as the K-Best, which offers a fixed complexity and a parallel implementation, thus making possible an implementation. However, this solution makes the detector to be sub-optimal since its leads to a performance loss compared to the ML detector. It is particularly true in the case of an inappropriate K according to the MIMO channel condition number, since the ML solution might be excluded from the search tree.
Since the complexity is fixed with such a detector, the exposed optimizations will induce a performance gain for a given neighbourhood size or a reduction of the neighbourhood size for a given Bit Error Rate (BER) goal. Common existing optimizations in the FNSA performance improvement are in particular the use of the Sorted QRD (SQRD) at the pre-processing step, and the Schnorr-Euchner (SE) enumeration strategy and the dynamic K-Best at the detection step.
However, although a neighbourhood sourly remains the one and only solution that achieves ML performance, it may lead to the use of a large size neighbourhood scan which would correspond to a dramatic increase of the computational complexity. This point is particularly true in the case of high order modulations.
Also, the SD must be fully processed for each transmit symbols vector detection over a given channel realization. A computational complexity reduction through adjacent-channel information re-use is not possible, even if the channel may be considered as constant over a certain block code size. Consequently, due to the SD's principle itself, the skilled man would have noticed the necessity of the computational complexity reduction of any SD-like detector for making it applicable in the LTE-A context.
A second technique which can be used for achieving near-ML performance is based on lattice reduction.
Document “Near-Maximum-Likelihood Detection of MIMO Systems using MMSE-Based Lattice-Reduction,” by Wübben, R. Böhnke, V. Kühm, and K.-D. Kammeyer, Communications, IEEE International Conference on, vol. 2, pp. 798-802, 2004 discloses the use of Lattice Reduction for the purpose of improving the conditioning of the channel matrix H and improving the efficiency of the detection process.
In particular the cited prior art document discloses the combination of a preprocessing phase depending on the channel followed by a linear MMSE equalization of the received symbols y.
In Wubben et al, the preprocessing phase comprises, in order to significantly reduce of the computational complexity the following steps:    1) apply a sorted and also extended QR decomposition of the matrix H (With QHQ=I and R being upper triangular) so as to generate Qext and Rext matrices which take into account the level of SINR (Signal to Interference and noise ratio) for the purpose of detecting first the layers having the best SINR ratio. In addition, the <<extended>> QR decomposition leads to the taking into account of the noise variance σ2 so as to improve the performance of the detection.    2) apply a lattice reduction algorithm—such as a Lenstra-Lenstra-Lovàsz algorithm) on the resulting SQRD decomposition so as to generate a matrix{tilde over (H)}=HT and to introduce a new vector Z=T−1x which results iny=Hx+n=HTT−1x+n={tilde over (H)}z+n     3) then processing the received symbols y by applying a MMSE linear detection on the resulting channel matrix {tilde over (H)} or even a Successive-Interference cancellation based on the conventional equation
            x      ^        SIC    =            argmin              x        ∈                  ξ                      n            T                                ⁢                                                                                Q                H                            ⁢              y                        -            Rx                                    2            .      The preprocessing phase suggested by Wübben of al. yields to both some efficiency for reducing the computational complexity of the detection process and some performance improvement.
However, the overall performance shows to be still far from the ideal ML-detection and it is therefore desirable to improve such preprocessing by an additional processing phase which significantly increases the performance of the detection while limiting the processing resources being required with the classical K-Best.